To find the equation of the line in the image, we can use the slope-intercept form of a line equation, $y = mx + b$, where:

• $m$ is the slope of the line
• $b$ is the y-intercept (the point where the line crosses the y-axis)

Step 1: Determine the slope $m$

We can calculate the slope by selecting two points on the line. From the graph:

• Point 1: $(-4, 0)$
• Point 2: $(0, -4)$

The formula for slope $m$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the coordinates of the two points: $m = \frac{-4 - 0}{0 - (-4)} = \frac{-4}{4} = -1$

Step 2: Find the y-intercept $b$

From the graph, the line crosses the y-axis at $(0, -4)$, so the y-intercept $b = -4$.

Step 3: Write the equation

Using the slope-intercept form $y = mx + b$ and substituting $m = -1$ and $b = -4$: $y = -x - 4$

Thus, the equation of the line is: $y = -x - 4$

Would you like more details on how this equation was derived or any other questions?

Here are some follow-up questions:

1. What is the significance of the slope in a line's equation?
2. How would the equation change if the slope was positive?
3. Can the slope be zero, and what would that represent graphically?
4. How can we find the x-intercept of a line from its equation?
5. What happens to the graph of a line if we change only the y-intercept?

Tip: Always ensure you accurately choose two points on the graph when calculating the slope for the best results.